Comparison between our approach and the UCLCHEM simulations. The x-axis denotes the input CRIR of each simulation, where the CRIR in each simulation is treated as uniform. The y-axis denotes the ratio between the calculated CRIR and the input one (${\tilde{\zeta }}_2/{\zeta }_2$) at t = 10⁶ yr. The black horizontal line represents the fiducial value and the horizontal dotted lines represent 50% of the deviation from the input values. Orange, green, and blue dashed lines represent results at T_k = 15, 50, and 100 K. Columns from left to right represent simulations with the cloud densities n_H = 10⁴, 10⁵, and 10⁶ cm⁻³. The large deviation at 15 K is due to the freeze-out processes that greatly reduce the gas-phase abundances of key species such as CO, thus, the chemical reactions we described in Sec. 2 are no longer satisfied.